% Mizar problem: t9_circcmb2,circcmb2,583,19 
fof(t9_circcmb2,conjecture,(
    ! [A,B,C] : 
      ( v1_relat_1(C)
     => ( r1_tarski(B,C)
       => ( v2_facirc_1(k4_xboole_0(A,B))
          | k4_xboole_0(A,C) = k4_xboole_0(A,B) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_facirc_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,cc3_facirc_1,cc4_facirc_1,commutativity_k2_tarski,commutativity_k2_xboole_0,commutativity_k3_xboole_0,d1_relat_1,d1_xboole_0,d2_facirc_1,d3_xboole_0,d4_xboole_0,d5_tarski,d7_xboole_0,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_tarski,dt_k2_xboole_0,dt_k3_xboole_0,dt_k4_tarski,dt_k4_xboole_0,dt_m1_subset_1,existence_m1_subset_1,fc10_facirc_1,fc12_relat_1,fc1_facirc_1,fc1_relat_1,fc2_facirc_1,fc2_relat_1,fc3_facirc_1,fc3_relat_1,fc4_relat_1,fc5_facirc_1,fc6_facirc_1,fc7_facirc_1,fc8_facirc_1,fc9_facirc_1,idempotence_k2_xboole_0,idempotence_k3_xboole_0,rc1_circcomb,rc1_facirc_1,rc1_funct_1,rc1_relat_1,rc2_facirc_1,rc2_funct_1,rc2_relat_1,rc3_facirc_1,rc3_funct_1,rc3_relat_1,rc4_funct_1,reflexivity_r1_tarski,symmetry_r1_xboole_0,t1_boole,t1_subset,t2_boole,t2_subset,t3_boole,t3_subset,t41_xboole_1,t45_xboole_1,t4_boole,t4_subset,t5_subset,t6_boole,t7_boole,t83_xboole_1,t8_boole]),
    [file(circcmb2,t9_circcmb2)]).

fof(antisymmetry_r2_hidden,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    []).

fof(cc1_facirc_1,axiom,(
    ! [A] : 
      ( v1_facirc_1(A)
     => ~ v1_xboole_0(A) ) ),
    file(facirc_1,cc1_facirc_1),
    []).

fof(cc1_funct_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_funct_1(A) ) ),
    file(funct_1,cc1_funct_1),
    []).

fof(cc1_relat_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_relat_1(A) ) ),
    file(relat_1,cc1_relat_1),
    []).

fof(cc2_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_xboole_0(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_funct_1(A) ) ) ),
    file(funct_1,cc2_funct_1),
    []).

fof(cc3_facirc_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ~ v2_facirc_1(A) ) ),
    file(facirc_1,cc3_facirc_1),
    []).

fof(cc4_facirc_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & ~ v2_facirc_1(A) )
     => ( v1_xboole_0(A)
        & v1_relat_1(A)
        & v1_funct_1(A)
        & v2_funct_1(A)
        & v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & ~ v3_xreal_0(A)
        & ~ v2_facirc_1(A) ) ) ),
    file(facirc_1,cc4_facirc_1),
    []).

fof(commutativity_k2_tarski,axiom,(
    ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ),
    file(tarski,k2_tarski),
    []).

fof(commutativity_k2_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ),
    file(xboole_0,k2_xboole_0),
    []).

fof(commutativity_k3_xboole_0,axiom,(
    ! [A,B] : k3_xboole_0(A,B) = k3_xboole_0(B,A) ),
    file(xboole_0,k3_xboole_0),
    []).

fof(d1_relat_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
    <=> ! [B] : ~ ( r2_hidden(B,A)
          & ! [C,D] : B != k4_tarski(C,D) ) ) ),
    file(relat_1,d1_relat_1),
    []).

fof(d1_xboole_0,axiom,(
    ! [A] : 
      ( A = k1_xboole_0
    <=> ! [B] : ~ r2_hidden(B,A) ) ),
    file(xboole_0,d1_xboole_0),
    []).

fof(d2_facirc_1,axiom,(
    ! [A] : 
      ( v2_facirc_1(A)
    <=> ? [B] : 
          ( v1_facirc_1(B)
          & r2_hidden(B,A) ) ) ),
    file(facirc_1,d2_facirc_1),
    []).

fof(d3_xboole_0,axiom,(
    ! [A,B,C] : 
      ( C = k3_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            & r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d3_xboole_0),
    []).

fof(d4_xboole_0,axiom,(
    ! [A,B,C] : 
      ( C = k4_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            & ~ r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d4_xboole_0),
    []).

fof(d5_tarski,axiom,(
    ! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) ),
    file(tarski,d5_tarski),
    []).

fof(d7_xboole_0,axiom,(
    ! [A,B] : 
      ( r1_xboole_0(A,B)
    <=> k3_xboole_0(A,B) = k1_xboole_0 ) ),
    file(xboole_0,d7_xboole_0),
    []).

fof(dt_k1_tarski,axiom,(
    $true ),
    file(tarski,k1_tarski),
    []).

fof(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    []).

fof(dt_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    []).

fof(dt_k2_tarski,axiom,(
    $true ),
    file(tarski,k2_tarski),
    []).

fof(dt_k2_xboole_0,axiom,(
    $true ),
    file(xboole_0,k2_xboole_0),
    []).

fof(dt_k3_xboole_0,axiom,(
    $true ),
    file(xboole_0,k3_xboole_0),
    []).

fof(dt_k4_tarski,axiom,(
    $true ),
    file(tarski,k4_tarski),
    []).

fof(dt_k4_xboole_0,axiom,(
    $true ),
    file(xboole_0,k4_xboole_0),
    []).

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    []).

fof(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    []).

fof(fc10_facirc_1,axiom,(
    ! [A,B] : 
      ( ( v1_facirc_1(A)
        & v1_facirc_1(B) )
     => ( ~ v1_xboole_0(k2_tarski(A,B))
        & v1_relat_1(k2_tarski(A,B)) ) ) ),
    file(facirc_1,fc10_facirc_1),
    []).

fof(fc12_relat_1,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0) ),
    file(relat_1,fc12_relat_1),
    []).

fof(fc1_facirc_1,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(k4_tarski(A,B))
      & v1_facirc_1(k4_tarski(A,B)) ) ),
    file(facirc_1,fc1_facirc_1),
    []).

fof(fc1_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k3_xboole_0(A,B)) ) ),
    file(relat_1,fc1_relat_1),
    []).

fof(fc2_facirc_1,axiom,(
    ! [A] : 
      ( ~ v1_facirc_1(A)
     => ( ~ v1_xboole_0(k1_tarski(A))
        & ~ v2_facirc_1(k1_tarski(A)) ) ) ),
    file(facirc_1,fc2_facirc_1),
    []).

fof(fc2_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k2_xboole_0(A,B)) ) ),
    file(relat_1,fc2_relat_1),
    []).

fof(fc3_facirc_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_facirc_1(A)
        & ~ v1_facirc_1(B) )
     => ( ~ v1_xboole_0(k2_tarski(A,B))
        & ~ v2_facirc_1(k2_tarski(A,B)) ) ) ),
    file(facirc_1,fc3_facirc_1),
    []).

fof(fc3_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k4_xboole_0(A,B)) ) ),
    file(relat_1,fc3_relat_1),
    []).

fof(fc4_relat_1,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0) ),
    file(relat_1,fc4_relat_1),
    []).

fof(fc5_facirc_1,axiom,(
    ! [A,B] : 
      ( ( ~ v2_facirc_1(A)
        & ~ v2_facirc_1(B) )
     => ~ v2_facirc_1(k2_xboole_0(A,B)) ) ),
    file(facirc_1,fc5_facirc_1),
    []).

fof(fc6_facirc_1,axiom,(
    ! [A,B] : 
      ( ~ v2_facirc_1(A)
     => ~ v2_facirc_1(k4_xboole_0(A,B)) ) ),
    file(facirc_1,fc6_facirc_1),
    []).

fof(fc7_facirc_1,axiom,(
    ! [A,B] : 
      ( ~ v2_facirc_1(A)
     => ~ v2_facirc_1(k3_xboole_0(A,B)) ) ),
    file(facirc_1,fc7_facirc_1),
    []).

fof(fc8_facirc_1,axiom,(
    ! [A,B] : 
      ( ~ v2_facirc_1(A)
     => ~ v2_facirc_1(k3_xboole_0(B,A)) ) ),
    file(facirc_1,fc8_facirc_1),
    []).

fof(fc9_facirc_1,axiom,(
    ! [A] : 
      ( v1_facirc_1(A)
     => ( ~ v1_xboole_0(k1_tarski(A))
        & v1_relat_1(k1_tarski(A)) ) ) ),
    file(facirc_1,fc9_facirc_1),
    []).

fof(idempotence_k2_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,A) = A ),
    file(xboole_0,k2_xboole_0),
    []).

fof(idempotence_k3_xboole_0,axiom,(
    ! [A,B] : k3_xboole_0(A,A) = A ),
    file(xboole_0,k3_xboole_0),
    []).

fof(rc1_circcomb,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A) ) ),
    file(circcomb,rc1_circcomb),
    []).

fof(rc1_facirc_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_facirc_1(A) ) ),
    file(facirc_1,rc1_facirc_1),
    []).

fof(rc1_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc1_funct_1),
    []).

fof(rc1_relat_1,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc1_relat_1),
    []).

fof(rc2_facirc_1,axiom,(
    ? [A] : ~ v1_facirc_1(A) ),
    file(facirc_1,rc2_facirc_1),
    []).

fof(rc2_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_xboole_0(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc2_funct_1),
    []).

fof(rc2_relat_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc2_relat_1),
    []).

fof(rc3_facirc_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & ~ v2_facirc_1(A) ) ),
    file(facirc_1,rc3_facirc_1),
    []).

fof(rc3_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A) ) ),
    file(funct_1,rc3_funct_1),
    []).

fof(rc3_relat_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A) ) ),
    file(relat_1,rc3_relat_1),
    []).

fof(rc4_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc4_funct_1),
    []).

fof(reflexivity_r1_tarski,axiom,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    []).

fof(symmetry_r1_xboole_0,axiom,(
    ! [A,B] : 
      ( r1_xboole_0(A,B)
     => r1_xboole_0(B,A) ) ),
    file(xboole_0,r1_xboole_0),
    []).

fof(t1_boole,axiom,(
    ! [A] : k2_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t1_boole),
    []).

fof(t1_subset,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(A,B) ) ),
    file(subset,t1_subset),
    []).

fof(t2_boole,axiom,(
    ! [A] : k3_xboole_0(A,k1_xboole_0) = k1_xboole_0 ),
    file(boole,t2_boole),
    []).

fof(t2_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,B)
     => ( v1_xboole_0(B)
        | r2_hidden(A,B) ) ) ),
    file(subset,t2_subset),
    []).

fof(t3_boole,axiom,(
    ! [A] : k4_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t3_boole),
    []).

fof(t3_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,k1_zfmisc_1(B))
    <=> r1_tarski(A,B) ) ),
    file(subset,t3_subset),
    []).

fof(t41_xboole_1,axiom,(
    ! [A,B,C] : k4_xboole_0(k4_xboole_0(A,B),C) = k4_xboole_0(A,k2_xboole_0(B,C)) ),
    file(xboole_1,t41_xboole_1),
    []).

fof(t45_xboole_1,axiom,(
    ! [A,B] : 
      ( r1_tarski(A,B)
     => B = k2_xboole_0(A,k4_xboole_0(B,A)) ) ),
    file(xboole_1,t45_xboole_1),
    []).

fof(t4_boole,axiom,(
    ! [A] : k4_xboole_0(k1_xboole_0,A) = k1_xboole_0 ),
    file(boole,t4_boole),
    []).

fof(t4_subset,axiom,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C)) )
     => m1_subset_1(A,C) ) ),
    file(subset,t4_subset),
    []).

fof(t5_subset,axiom,(
    ! [A,B,C] : ~ ( r2_hidden(A,B)
      & m1_subset_1(B,k1_zfmisc_1(C))
      & v1_xboole_0(C) ) ),
    file(subset,t5_subset),
    []).

fof(t6_boole,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => A = k1_xboole_0 ) ),
    file(boole,t6_boole),
    []).

fof(t7_boole,axiom,(
    ! [A,B] : ~ ( r2_hidden(A,B)
      & v1_xboole_0(B) ) ),
    file(boole,t7_boole),
    []).

fof(t83_xboole_1,axiom,(
    ! [A,B] : 
      ( r1_xboole_0(A,B)
    <=> k4_xboole_0(A,B) = A ) ),
    file(xboole_1,t83_xboole_1),
    []).

fof(t8_boole,axiom,(
    ! [A,B] : ~ ( v1_xboole_0(A)
      & A != B
      & v1_xboole_0(B) ) ),
    file(boole,t8_boole),
    []).